SECTION 1
Why Estimation Matters
People have used estimation (making a close guess based on rounding) for thousands of years. Ancient builders estimated the number of stones they needed for walls. Merchants estimated the cost of goods before adding up every coin. Estimation has always been a quick way to check whether an answer "makes sense."
On timed tests like the SHSAT, estimation is your secret weapon. You can't spend five minutes re-solving every problem. Instead, you round the numbers, do quick mental math, and see if your answer lands in the right neighborhood. If it doesn't, you know you made a mistake somewhere.
3000 BCE • Ancient Egyptian Builders
1600s • Scientific Revolution
1900s • Fermi Estimation
Today • Standardized Test Strategy
The big question estimation answers is simple: "Does my answer make sense?" If you calculate that a shirt costs $4,000 or that a person runs 500 miles per hour, estimation would have caught those errors instantly.
SECTION 2
Core Principles of Estimation
Estimation is not about getting the exact answer. It's about getting a reasonable range — a ballpark — so you can tell whether your precise answer is close or way off. Here are the key ideas you need to know.
Round to Friendly Numbers
Preserve the Operation
Compare, Don't Replace
Balance Your Rounding
KEY TAKEAWAY
SECTION 3
Seeing Estimation in Action
The diagram below shows how estimation works as a checking tool. You start with the original problem, round the numbers, do quick math, and then compare your estimate to your calculated answer.
Notice the decision point in the middle. "Close enough" doesn't mean your estimate matches exactly. It means the estimate and your answer are in the same ballpark. For example, if your estimate is about 200 and your exact answer is 193, that's reasonable. But if your estimate is 200 and your answer is 1,930, something went wrong.
SECTION 4
The Math Behind Estimation
Estimation relies on rounding — replacing a number with a nearby "friendly" number. Here are the key rounding rules you'll use.
BASIC ROUNDING RULE
Example: 487 rounded to the nearest hundred → 500 (because 8 ≥ 5). 423 rounded to the nearest hundred → 400 (because 2 < 5).
ESTIMATION FORMULA
Replace each number in the problem with its rounded version, then perform the same operations (add, subtract, multiply, or divide).
REASONABLENESS CHECK
The vertical bars | | mean "the distance between." If the gap between your answer and your estimate is small compared to the size of the numbers, you're on track.
SHSAT Tip
SECTION 5
Rounding Strategies for Different Operations
Different math operations call for slightly different rounding strategies. The diagram below shows how rounding affects addition versus multiplication and why balanced rounding matters.
Look at the bottom-right panel carefully. A student multiplied 48 × 21 and got 108 — but the estimate says the answer should be near 1,000. That huge gap means the student made an error. In this case, they forgot to carry and only computed 48 × 2 + 48 × 1 incorrectly. Estimation saved them from picking a wrong answer.
| Operation | Best Rounding Strategy | Example |
|---|---|---|
| Addition | Round each number to the nearest ten or hundred | 487 + 312 → 500 + 300 = 800 |
| Subtraction | Round both numbers the same way | 843 − 397 → 840 − 400 = 440 |
| Multiplication | Round one up and one down to balance | 48 × 21 → 50 × 20 = 1,000 |
| Division | Round to make a "nice" division fact | 623 ÷ 19 → 600 ÷ 20 = 30 |
Recommended rounding approaches for each operation
SECTION 6
Worked Example: Multi-Step Word Problem
Let's walk through a full SHSAT-style word problem and use estimation to check our answer.
Problem
Full Solution With Estimation Check
- 1
Step 1 — Find the total number of each item
Total notebooks: 23 × 18 = 414. Total folders: 23 × 12 = 276.414 notebooks, 276 folders - 2
Step 2 — Find the cost of each type of supply
Notebook cost: 414 × $2.89 = $1,196.46. Folder cost: 276 × $1.15 = $317.40.Notebooks = $1,196.46, Folders = $317.40 - 3
Step 3 — Add to find total cost
$1,196.46 + $317.40 = $1,513.86.Total cost = $1,513.86 - 4
Step 4 — Estimate to check reasonableness
Round: 23 classrooms → 20. Notebooks per class: 18 → 20. Folders per class: 12 → 10. Notebook price: $2.89 → $3. Folder price: $1.15 → $1. Now estimate: Notebooks cost ≈ 20 × 20 × $3 = $1,200. Folders cost ≈ 20 × 10 × $1 = $200. Total estimate ≈ $1,200 + $200 = $1,400.Estimate ≈ $1,400 - 5
Step 5 — Compare exact answer to estimate
Exact answer: $1,513.86. Estimate: $1,400. These are in the same ballpark — both are between $1,000 and $2,000. The exact answer is a bit higher because we rounded the number of classrooms down (from 23 to 20), which lowered the estimate. This makes sense!✓ $1,513.86 is reasonable!
WHY THIS WORKS
SECTION 7
When Estimation Helps and When It Doesn't
Estimation is powerful, but it has limits. Knowing when to use it — and when to be extra careful — will help you make the most of this strategy on the SHSAT.
| Strengths ✓ | Limitations ✗ |
|---|---|
| Catches big arithmetic mistakes (wrong number of zeros, misplaced decimals) | Won't catch small errors (like adding 3 instead of 4) |
| Takes only 10–20 seconds per problem | Can be misleading if you round too aggressively |
| Eliminates wildly wrong multiple-choice options | Doesn't help when answer choices are very close together |
| Builds number sense and confidence | Requires you to understand the problem setup first |
Strengths vs. limitations of estimation as a checking strategy
WHEN TO USE ESTIMATION ON THE SHSAT
SECTION 8
Connecting to Bigger Ideas
Estimation on the SHSAT is a stepping stone to bigger mathematical ideas. As you move into high school and beyond, the habit of checking for reasonableness becomes even more important.
| SHSAT Estimation | High School & Beyond |
|---|---|
| Round numbers and do quick mental math | Use order-of-magnitude estimates (Is the answer in the tens, hundreds, or thousands?) |
| Check if answer choices are reasonable | Verify solutions by plugging them back into equations |
| Use friendly numbers like 10, 20, 100 | Use significant figures and scientific notation |
| Catch arithmetic errors in word problems | Validate complex models in science and engineering |
How estimation grows with you
In physics, scientists use estimation to check whether a formula gives a sensible result. In finance, adults estimate to make sure a bill looks correct. The skill you build now — asking "Does this answer make sense?" — is one you will use for the rest of your life.
SECTION 9
Practice Problems
Try these five problems. For each one, solve the problem exactly, then use estimation to check whether your answer is reasonable.
Question 1: CONCEPTUAL
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Question 2: BASIC CALCULATION
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Question 3: INTERMEDIATE
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Question 4: APPLIED
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Question 5: CRITICAL THINKING
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SUMMARY
Lesson Summary
Summary
Estimation is the practice of rounding numbers and doing quick mental math to check whether an answer is reasonable. On the SHSAT, you can use it after solving a problem to catch big mistakes, or before solving to eliminate wrong answer choices. The key steps are: round each number to a friendly number, perform the same operations, and compare your estimate to your exact answer.
Remember to balance your rounding — if you round one number up, try to round another down. Estimation catches errors like misplaced decimals and extra zeros, but it won't catch tiny arithmetic slips. Always ask yourself: "Does this answer make sense?" That one question can save you points on test day.